A grocery store associate manually takes inventory
By Michael Watson, Ph.D., Adjunct Professor at Northwestern University / Author / Business Advisor | June 27, 2024

Six Features of a Good Inventory Formula and Five Features You Can Ignore

How many are you missing – or mistakenly – using?

The blessing and curse of inventory science is the number of different formulas and models.

The blessing is that there is a model and research to support thousands of different nuances.

The curse is that this confuses practitioners and companies getting started, whether they’re in retail, manufacturing, warehousing, healthcare, energy, or even government. And even worse, companies can waste time and money implementing nuanced policies that aren’t better than a simple model.

As I mentioned in a previous post, my opinion is controversial: the formula should only be good enough.

A “good enough” formula is the right place to start for most companies. And, for most of those companies, this starting point will be the long-term solution.

The six features of a “good enough” model are expected demand, demand forecast error, average lead time, lead time standard deviation, review period (or fixed order size), and desired fill rate.

These are the big inventory drivers; you should work hard to collect this data.

Standard textbook formulas take all these data points and return the proper safety stock and, by extension, your order policies. Of course, there are still some nuances here, but these six features keep it to the most important.

Here are a few notes on these features:

If you don’t have the demand forecast error, you can substitute the standard deviation of demand. This will not make statisticians happy, but it is a good enough workaround for most firms.

The lead time and its standard deviation are more challenging to calculate than you think. In many ERP systems, this will be a static input (with no information on the standard deviation). If you have to, start with that data. Then, use your actual data to calculate a dynamic lead time. Lead time and its variability are too important to rely on static inputs.

The review period is the time between placing orders. For example, if you order products once a week, your review period is one week. This time is added to the lead time.

It is easy to think of the fill rate as some precise dial— that is, you can have some products with a 98.2% fill rate and others with a 98.6%. I think there will be so much noise in your data that you are better off just having a few settings for fill rate: 99.9% (very high), 99% (high), 97% (medium), 95% (medium-low), and 90% (low). If you want to add something like 70% (you are ok with a lot of stockouts) or 50% (you don’t want safety stock), that works too.

You should monitor the system to look for ways to improve your data and finetune the safety stock by changing the fill rate. You can use the fill rate to adjust the safety stock. For example, if inventory seems too high, lower the fill rate, or raise the fill rate if you are stocking out too much.

If you start with the above, you may have a system that will work for years. Or, you will at least have a solid foundation to understand what you need to do next.

I should also mention what five features to ignore. You will be able to ignore some of these features forever. For others, consider revisiting. This advice might get me in trouble with inventory experts, but here it goes:

1. The order cost: This feature comes from the desire to optimize the order size. This comes from the economic order quantity (EOQ) model. You can ignore this because you’ve optimized the order size by setting a review period or because you already have a reasonable order size (the EOQ results are robust – meaning that a reasonable order size is close to optimal). Additionally, order costs can be complicated to calculate… all for a number that won’t have a big impact.

2. The normal distribution: I’ve seen people get worried that the standard formulas assume the normal distribution. We think of the normal distribution as a nice bell curve, and everyone’s experience with variability is far from a nice bell curve. However, the normal distribution is conservative when the standard deviations are high – it flattens out quickly. This means that the assumption of the normal distribution tends to err on the high side. This is the good side – having too much inventory rather than too many stockouts is usually better. You can fix this by tuning the fill rate.

3. Back orders versus lost orders: There are some differences in the formulas depending on whether you assume that stockouts lead to backorders (you still have to fill) or lost sales. My experience is that the difference doesn’t change much.

4. The cost of lost sales: Some models, like the famous News Vendor Model, use the cost of lost sales to determine inventory levels. However, the cost of a lost sale is hard to estimate. And, even when people estimate this, they often are upset that this number suggests missing more sales than they are willing to. This tells me that many intangibles go into this measure – including having the CEO yell at you for too many stockouts. So, the fill rate is much easier for a company to use and understand.

5. Multi-echelon optimization: This is worth a series of posts. I’ll just say that the standard inventory formulas allow you to calculate the inventory across different echelons successfully. And this inventory level will be optimal given your current policies. Multi-echelon inventory optimization is probably best to run annually (or something like that) to reset where you buffer inventory (and where you don’t). You can’t change this every week.

There is much more to say on this topic, probably a book’s worth. In future posts, I’ll cover these topics, low volume, seasonality, and various other topics.


Editor's Note: 

If you've missed past posts from Michael, catch up now:

Blog, Article, Retail, Manufacturing, Warehouse and Distribution, Transportation and Logistics, Public Sector, Healthcare, Hospitality,

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